Probability of gene identity by descent: computation and applications.

Two-locus and three-locus gene identity by descent in pedigrees.

Although there have been several mathematical formulations of multilocus segregation, multilocus gene identity by descent in pedigrees has been little considered. Here we present a computationally feasible algorithm for the computation of two-locus kinship for individuals between whom there may be multiple complex relationships, and use it to investigate patterns of two-locus gene identity by d...

Recombination, gene conversion, and identity-by-descent at three loci.

We investigate the probabilities of identity-by-descent at three loci in order to find a signature which differentiates between the two types of crossing over events: recombination and gene conversion. We use a Markov chain to model coalescence, recombination, gene conversion and mutation in a sample of size two. Using numerical analysis, we calculate the total probability of identity-by-descen...

An Enhanced HL-RF Method for the Computation of Structural Failure Probability Based On Relaxed Approach

The computation of structural failure probability is vital importance in the reliability analysis and may be carried out on the basis of the first-order reliability method using various mathematical iterative approaches such as Hasofer-Lind and Rackwitz-Fiessler (HL-RF). This method may not converge in complicated problems and nonlinear limit state functions, which usually shows itself in the f...

A graphical algorithm for fast computation of identity coefficients and generalized kinship coefficients

UNLABELLED Computing the probability of identity by descent sharing among n genes given only the pedigree of those genes is a computationally challenging problem, if n or the pedigree size is large. Here, I present a novel graphical algorithm for efficiently computing all generalized kinship coefficients for n genes. The graphical description transforms the problem from doing many recursion on ...

A Revised Li-Sacks Formula For Calculating the Probability of Identity-by-Descent Proportion